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1 TIME, SYMMETRY OF Although everyday experience leads us to believe that time "flows" in one direction, the equations of both classical and modern physics work equally well in either time direction. Since these equations accurately describe all observations of physical phenomena, from those made with the human eye to those made with the finest scientific instruments, the implication is that time can flow either way. The arrow of time of human experience (see also Time, Arrow of) results from the fact that macroscopic objects contain many particles and these, to a great extent, move about randomly. The probability for a phenomenon happening in one time direction, such as air escaping from a punctured tire, is often much greater than the probability for the phenomenon happening in the opposite time direction, such as outside air re-inflating a punctured tire. The reverse time event is not impossible, just highly unlikely. The arrow of time is defined as the direction of most probably occurrences. At the level of chemical, nuclear, and elementary particle interactions, however, reactions occur in either time direction. Statistical differences between initial and final states can result in different reaction rates for the two directions, but at the basic interaction level the two directions are equally likely. One exception occurs in certain elementary particle reactions that are mediated by the weak nuclear force (see also Time, Asymmetry of). There a slight asymmetry of one part on a thousand exists. However, reactions can still proceed in either direction with only a slight difference in probabilities.

2 In 1949 Richard Feynman showed that an antiparticle, such as the antielectron or positron, may be viewed as a particle going backward in time. This symmetry is built into the visual aids called Feynman diagrams used by physicists to calculate the rates of various reactions between elementary particles. Despite the basic time symmetry of physics, most physicists continue to assume directed time in their models. This generally makes no difference, since a particle going backward in time is empirically indistinguishable from its antiparticle going forward in time, where "forward" is defined by everyday experience. However, it has been known for decades that quantum mechanics predicts certain phenomena that seem paradoxical. For example, electrons and other particles behave as if they can be in two or more places at the same time. Experiments have been performed that suggest "backward causality," where the changing of the parameters of a detector after the particles to be detected are already in flight affects the behavior of those particles, even though they cannot be reached without sending a superluminal signal (signal traveling faster than the speed of light, violating Einstein's theory of special relativity). This is taken as evidence for nonlocality in quantum mechanics, in which two events separated in space are still connected despite the fact that no signal can pass between them without going faster than the speed of light. Time-reversibility offers a possible explanation for these observations. For example, an electron can be seen to appear at two places at the same time when one uses the picture introduced by Feynman, as illustrated in figure 1. An electron

3 moving through space can be turned back in time by a collision with a photon. Normally this is simply viewed as the production of an electron-positron pair. However, we can view the positron as an electron going backward in time. If, in the "past," it is reversed again by a collision with a photon, it can proceed forward in time again, thus appearing two places at once. Figure 1. The "Feynman space-time zigzag." In (a), an electron goes forward in time, scatters off a photon, moves backward in time, scatters again, and goes forward. Note that the electron appears simultaneously in three different places at time B. In (b), the conventional time-directed view is shown in which an electron-positron pair is produced at time A, with the positron annihilating with the other electron at time C. The advantage

4 of view (a) is parsimony, with no need to introduce antiparticles. It also offers an explanation for the indistinguishability of electrons. If we insist on a single time direction, an electron appearing two places at once implies superluminal motion (motion faster than the speed of light), which is forbidden by Einstein's theory of relativity. Indeed, in this case infinite speed is needed. While relativity does in principle allow for superluminal motion, it is restricted to particles called tachyons that must always travel faster than the speed of light. Particles, such as electrons, which normally travel at less than the speed of light cannot be accelerated beyond that speed. In any case, no tachyons have ever been observed. In short, time reversibility is not forbidden and indeed is suggested by the basic principles of physics. Furthermore, time reversibility can help to explain the so-called paradoxes of quantum mechanics, what Einstein called "spooky action at a distance," without involving superluminal motion. Still, one problem remains to be resolved: the time travel or grandfather's paradox. Simply stated, if you could go back in time, you would be able to kill your grandfather before he met your grandmother, in which case you would never have been born! The answer to this paradox is rather subtle and has to do with the definition of the arrow of time. Time's arrow is determined by the direction in which the entropy of the universe increases. Entropy is a measure of disorder. Negative

5 entropy is thus a measure of order or information. Thus time's arrow is the direction in which information decreases. Now, if you were to go "backward" with respect to the conventional direction of time to kill your grandfather, you would be using information from the future that was not available in the past. This implies that the future has more information lower entropy than the past, a contradiction. That is, it would not be the future but the past by definition. If you traveled back without any information, as if you had amnesia and did not even know your own name, there would be no contradiction but you would have no way of identifying your grandfather. FURTHER READING Davies, Paul. (1996). About Time: Einstein's Unfinished Revolution. New York: Simon & Schuster. Feynman, Richard. (1985). QED: The Strange Theory of Light and Matter. Princeton: Princeton University Press. Lederman, Leon M. and Christopher T. Hill. (2004). Symmetry and the Beautiful Universe. Amherst, NY: Prometheus Books. Price, Huw. (1996). Time's Arrow and Archimedes Point: New Directions for the Physics of Time. Oxford: Oxford University Press. Stenger, Victor J. (2000). Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Amherst, NY: Prometheus Books.

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